Maybe the problem wasn’t your PC?
Ok just kidding, but seriously is your PC crashing or just the game? Try windows+L or ctrl+alt+delete. If none of the above work and num-lock has no effect on the keyboard lights, then it’s your whole PC that crashed.
If that’s the case, start by removing any overclocks if they are set up. Second, do you have multiple hard disks? If so, put Steam on the most stable HDD (same as Skyrim maybe?) reinstall/extract BM again and use steam to verify the Valve game files.
Third, maybe you need to upgrade your GPU drivers or chipset drivers. Other than that, maybe your PC just doesn’t like Black Mesa in its current setup due to a recent Valve update (I know they moved from the GCF file format among other things).
If you lose your saves, you can resume the same chapter by using sv_unlockedchapters command in console.